This invention relates to a method and apparatus for determining one or more statistical estimators of customer behavior. The invention is particularly related to, but in no way limited to, modeling customer behavior using a Bayesian statistical hidden Markov model technique.
Businesses typically have records of customer transaction histories. These records contain information that is potentially very valuable to the business because it enables the business to analyze customer behavior and use this “feedback” to help plan the future of the business. However, assessments of the available data only provide information about customer behavior that has already occurred. This is a drawback because behavior patterns typically change over time. For example, a customer who is at present not very profitable could become more profitable in the future. There is thus a need to predict the future behavior of customers.
One particular example concerns a business such as a bank which wishes to predict when a customer is likely to leave the bank. In that case such a prediction would be extremely advantageous because it allows the bank to take action such as to give incentives to the customer to prevent them from leaving.
Bayesian statistical techniques have been used to “learn” or make predictions on the basis of a historical data set. Bayes' theorem is a fundamental tool for a learning process that allows one to answer questions such as “How likely is my hypothesis in view of these data?” For example, such a question could be “How likely is a particular future event to occur in view of these data?”
Bayes theorem is written as:       P    ⁡          (              H        /        data            )        =                    P        ⁡                  (                      data            /            H                    )                    ⁢              P        ⁡                  (          H          )                            P      ⁡              (        data        )            
Which can also be written as:P(H/data)∝P(data/H)·P(H)
Because P(data) is unconditional and thus does not depend on H.
The probability of H given the data, P(H/data) is called the posterior probability of H. The unconditional probability of H, P(H) is called the prior probability of H and the probability of the data given H, P(data/H) is called the likelihood of H. By using knowledge and experience about past data an assessment of the prior probability can be made. New data is then collected and used to update the prior probability following Bayes theorem to produce a posterior probability. This posterior probability is then a prediction in the sense that it is a statement about the likelihood of a particular event occurring in the future. However, it is not simple to design and implement such Bayesian statistical methods in ways that are suited to particular practical applications.